The main objective of this study is to provide patients that have refractory rheumatoid arthritis with a better treatment option. Rheumatoid arthritis affects 1-2 percent of the population, and current treatments are inadequately efficacious for many patients. Immunosuppressive agents have been shown to clearly suppress the immunopathogenic mechanisms response for much of the disease activity. This is a clinical trial to determine the maximally tolerated dose of 5-FU and leucovorin when given on a daily x 5 schedule in patients with rheumatoid arthritis, to define toxicity and to document any clinical benefit of this drug combination in patients with rheumatoid arthritis.